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A298304
Number of rooted trees on n nodes with strictly thinning limbs.
6
1, 1, 1, 2, 3, 4, 7, 12, 19, 31, 51, 85, 144, 245, 417, 712, 1221, 2091, 3600, 6216, 10763, 18691, 32546, 56782, 99271, 173849, 304877, 535412, 941385, 1657069, 2919930, 5150546, 9093894, 16071634, 28428838, 50331137, 89181251, 158145233, 280650225, 498410197
OFFSET
1,4
COMMENTS
An unlabeled rooted tree has strictly thinning limbs if its outdegrees are strictly decreasing from root to leaves.
LINKS
EXAMPLE
The a(7) = 7 trees: (oo(o(o))), (o(o)(oo)), (ooo(oo)), ((o)(o)(o)), (oo(o)(o)), (oooo(o)), (oooooo).
MATHEMATICA
stinctQ[t_]:=And@@Cases[t, b_List:>Length[b]>Max@@Length/@b, {0, Infinity}];
strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], stinctQ]];
Table[Length[strut[n]], {n, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 16 2018
EXTENSIONS
a(26)-a(40) from Alois P. Heinz, Jan 17 2018
STATUS
approved